Trabecular bone adaptation in a finite element frame model using load dependent fabric tensors

Most human bones are divided into an external cortical and an internal trabecular substance. Both kinds of bone tissue are capable of adapting their strength to the loads acting upon them; they are in a state of continuous remodelling. The present study introduces a new method for modelling the functional adaptation of the trabecular bone by means of a finite element frame model, where each trabecula is represented by one beam element in order to achieve a relatively simple model with a low element number. The model is generated in a stochastic way, thus avoiding the need for CT imaging. For the purpose of the remodelling simulations a structure consisting of two kinds of beam elements is used. The elements involved in carrying loads are called ‘active’ beams, while those not working are regarded as ‘passive’ beams. Any modification in the structure is executed by changing the active elements into passive or vice versa according to the eigenvalues of node-by-node defined fabric tensors. The algorithm generates anisotropic structures, with load-directed beam orientations similar to the living trabecular bone tissue.